# A and B can do a piece of work in 15 days; B and C in 12 days; C and A in 20 days. How many days will be taken by A, B and C

57 views

closed

A and B can do a piece of work in 15 days; B and C in 12 days; C and A in 20 days. How many days will be taken by A, B and C working together to finish the work?

+1 vote
by (31.0k points)
selected by

Number of days required by A and B to finish the work : 15 days

Number of days required by A and B to finish the work : 12 days

Number of days required by A and B to finish the work : 20 days

Work done by A and B in one day: $\frac{1}{15}$

Work done by B and C in one day: $\frac{1}{12}$

Work done by C and A in one day: $\frac{1}{20}$

Work done by (A and B) , (B and C ) and (C and A) in one day that is work done by

(A + B) + (B + C) + (C + A) = 2(A + B + C) = $\frac{1}{12}+\frac{1}{12}+\frac{1}{20}=\frac{12}{60}=\frac{1}{5}$

Work done by A, B and C = $\frac{1}{2}\times\frac{1}{5}=\frac{1}{10}$

∴ They can do the work in 10 days